An oft-repeated argument on both theistic and atheistic sides is that "Absence of evidence is not evidence of absence". This is usually presented as a part of an accepted premise - "you can't prove a negative".
Now, I'd like to put this statement in perspective and divide the so-called unprovable statements into two categories.
1. Statements with a subject so ill-defined, generic and changeable that neither it's positive nor its negative form are provable.
2. Statements which are provable in the positive form.
Let's take the case of Russell's teapot. Assume that it is a standard-issue, 19th century white-china teapot with floral patters, having the capacity to hold 500 ml of water and it is to be found between the orbits of Mars and Jupiter. With a specific definition of Russell's teapot like this and with advanced enough technology, we can take a picture of the the whole area between Mars and Jupiter and with good enough resolution, look for the teapot. If we see such a teapot, the positive claim - "There is a Russell's teapot" would be proven. But is we don't find it, the negative claim - "There is no Russell's teapot" would be proven as well. If it did exist, it would've been seen in the image.
This may not apply to all the cases due to imprecise attributes or limitations of technology, but I believe we can safely say that "Absence of evidence is not evidence of absence unless presence of such evidence can be reasonably expected". Further, I'd add - "Yes, you can prove a negative in some cases". Thus, I'd say that when theists argue "You can't prove that god doesn't exist", instead of replying with "You can't prove a negative", we should say "Come up with a precise enough definition and we will".
Now, I'd like to put this statement in perspective and divide the so-called unprovable statements into two categories.
1. Statements with a subject so ill-defined, generic and changeable that neither it's positive nor its negative form are provable.
2. Statements which are provable in the positive form.
Let's take the case of Russell's teapot. Assume that it is a standard-issue, 19th century white-china teapot with floral patters, having the capacity to hold 500 ml of water and it is to be found between the orbits of Mars and Jupiter. With a specific definition of Russell's teapot like this and with advanced enough technology, we can take a picture of the the whole area between Mars and Jupiter and with good enough resolution, look for the teapot. If we see such a teapot, the positive claim - "There is a Russell's teapot" would be proven. But is we don't find it, the negative claim - "There is no Russell's teapot" would be proven as well. If it did exist, it would've been seen in the image.
This may not apply to all the cases due to imprecise attributes or limitations of technology, but I believe we can safely say that "Absence of evidence is not evidence of absence unless presence of such evidence can be reasonably expected". Further, I'd add - "Yes, you can prove a negative in some cases". Thus, I'd say that when theists argue "You can't prove that god doesn't exist", instead of replying with "You can't prove a negative", we should say "Come up with a precise enough definition and we will".
